Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.

@article{Stojkoski2021GeometricBM,
  title={Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.},
  author={Viktor Stojkoski and Trifce Sandev and Ljupco Kocarev and Arnab K. Pal},
  journal={Physical review. E},
  year={2021},
  volume={104 1-1},
  pages={
          014121
        }
}
We study the effects of stochastic resetting on geometric Brownian motion with drift (GBM), a canonical stochastic multiplicative process for nonstationary and nonergodic dynamics. Resetting is a sudden interruption of a process, which consecutively renews its dynamics. We show that, although resetting renders GBM stationary, the resulting process remains nonergodic. Quite surprisingly, the effect of resetting is pivotal in manifesting the nonergodic behavior. In particular, we observe three… Expand

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